VELOCITY OF HYDROLYSIS OF ETHYL ACETATE
2193
5 . An excess of ammonia favors the inclusion of silica in the ammonia precipitate, but this has a slightly solvent action on the aluminum hydroxide. 6. A Sorensen value of from 7 to 8, as shown by a pink color with rosolic acid, is advised in making the ammonia precipitation. 7. A very small quantity of silica, roughly 0.3 mg., escapes precipitation, and an equal quantity is generally found in the wash waters from the ammonia precipitate. 8. In rock analysis a single evaporation with hydrochloric acid is sufficient, provided silica is also determined in the ammonia precipitate. WASHINGTON, D. C. [CONTRIBUTION FROM THE JOHN HARRISON LABORATORY OF CHEMISTRY OF THE UNIVERSITY OF PENNSYLVANIA ]
A STUDY OF THE VELOCITY OF HYDROLYSIS OF ETHYL ACETATE BY HERBERTS. HARNEDAND ROBERTPFANSTIEL~ Received July 11, 1922
From various considerations regarding the independent character of the ions in dilute solutions, MacInnes2 has assumed that, in dilute solutions of the same molality of hydrochloric acid and potassium chloride, the chloride ion has the same activity. Further, he assumed that in a solution of potassium chloride of a given strength, the activities of the potassium and chloride ions are the same. Harned3 found evidence from electromotive-force data for the validity of these assumptions in conc. solutions and calculated the individual activity coefficients of the ions of these electrolytes. If these assumptions are correct, it follows from these calculations that the activity coefficient of the hydrogen ion in solutions of hydrochloric acid decreases with increasing concentration until a concentration of 0.15 M is reached, and then increases. In many recent s t ~ d i e s the , ~ contention has been made that the velocities of homogeneous reactions catalyzed by ions are a function of the ion activities and not the ionic concentrations. It has been pointed out by Jones and Lewis that other causes such as “the water displacement effect” may also influence the reaction velocity. From this point of view, 1 Presented t o the Faculty of the Graduate School of the University of Pennsylvania by Robert Pfanstiel in partial fulfilment of the requirements for the degree of Doctor of Philosophy. * MacInnes, THISJOURNAL, 41, 1086 (1919). 8 Harned, ibid., 42, 1808 (1920). 4 (a) Harned, ibid., 40, 1461 (1918). (b) Jones and Lewis, J . Chem. Soc., 43, 2387 (1921). (d) Akerlof, Z. 117, 1120 (1920). (c) Scatchard, THISJOURNAL, 44, 1475 (1922); physik. Chem., 98, 260 (1921). (e) Harned and Seltz, THISJOURNAL, etc.
2194
HERBERT S. HARNED AND ROBERT PFANSTIEL
a study of the hydrogen-ion catalysis of a simple ester in aqueous solution should afford information regarding the individual activity coefficient of the hydrogen ion. Owing to secondary influences such as “the water displacement effect,” i t is not to be expected that exact relationships are to be found immediately. Earlier work on this subject is of considerable interest. A compilation of previous data taken from the work of Taylor,b Kay,6 and Lunden? on the hydrolysis of ethyl acetate and oth’er esters is contained in a paper by Schreiner.8 The results in this paper on the velocity of hydrolysis of ethyl acetate by hydrochloric acid of concentration G are reproduced in Table I. TABLE I SCHREINER’S COMPILATION lo5
C
Mols. per liter
Oi
1
0.010 2.93 293 0.025 6.99 280 0.050 278 13.83 0.100 283 28.29 0.132 38.1 288 43.2 288 0.150 285 0.200 57.0 0.250 71.6 286 0.479 288 138.0 0.493 145.0 296 K’IF, is the observed monomolecular velocity constant obtained by the formula A
log A T X ’
Thus, the velocity constant divided by the concentration passes through a minimum a t about 0.1 M hydrochloric acid concentration. This is similar to the behavior of the activity coefficient of the hydrogen ion as mentioned above. This evidence is by no means conclusive, but is suggestive owing to the parallelism between these properties. Consequently, further careful work has been undertaken. Apart from the above considerations, the data accumulated in the present research will help to a considerable extent to supplement what has been done, especially,the excellent study of Griffith and Lewisgon the velocity of hydrolysis of methyl acetate.
General Theory For the present purpose, it will suffice if we assume that the velocity ob hydrolysis of the ester proceeds according to the equation v1 = klaea’naw Taylor, Medd. K . Vetenskapsakad i\’ohelinst., 2, No. 37 (1913). Kay, Proc. Roy. SOC.Edinburgh, 22, 484 (1897). Lunden, Z . physik. Chem., 49, 189 (1904). *Schreiner, Z . anorg. Chem., 116, 102 (1921). Griffith and Lewis, J . Chem. SOC.,109, 67 (1916).
6
(1)
VELOCITY OF HYDROLYSIS OF BTHYL ACETATE
2192
where a,, a t H , and a, are the activities of the ester, the hydrogen ion and water, respectively, in the solution; VI is the velocity, and kl the velocity constant of hydrolysis. This follows from the activity theory of homogeneous catalysis,4” on the assumption that we are dealing with a simple hydrogen-ion catalysis, and that the water enters to the first power. Since, by definition, F,c equals a, where F , is the activity coefficient of the ester and c is its concentration, substitution in (1) gives vl = klFeca’Haw
(2)
At a given temperature k l remains constant under changing conditions of all other factors in Equation 2. Let k’1 = klaHawor Substituting in (2) gives 4
K’iFeC
(4)
From (3), k t l is proportional to atHand a,. During the course of reaction in a given experiment, atH and a, remain constant,lO,and therefore FE’1 represents the velocity constant in each experiment. But the velocity constant is obtained by measurement of c, and, consequently, Equation 4 shows that kflFe instead of k f l is obtained in an actual measurement. Therefore, in all tables, ktlF, will always denote the observed velocity constant. F, probably remains constant in a solution containing hydrochloric acid a t a given concentr&tion, because ktlF, is practically constant when obtained by Equation 4. F , may vary with a change in hydrochloric acid concentration, and thus k‘lF,/afHa, will vary, according to Equation 3. F, can be determined from measurements of the solubility1’ of the ester in different strengths of hydrochloric acid, as can be seen from the following thermodynamic reasoning. The activity of the ester in a saturated solution in the presence of the liquid ester a t the same pressure and temperature will always have the same value. Therefore, if F’,, F”,, F” ’e, etc., represent the activity coefficients of the ester in solutions containing acid at different concentrations, S’,S“,S“’, etc., represent the concentrations of the ester in the saturated solutions, or the solubilities, then F’eS’ = FIfeS” = F’’’eS’’’ = FeS = constant (5) The simplest convention to adopt in measuring F , is to let the constant equal “1”. Then Thus, if F, varies with the concentration of acid, it is necessary t o multiply 10 This assumption is justiiied because, in an actual experiment, k’l F. is independent of the time. 1 1 Fe could also be obtained by measurement of the partial vapor pressure of the ester.
2196
HERBERT S. HARNED AND ROBERT PFANST4L
ktlF,, the observed velocity constant, by the solubility, or l/Fe, in order to obtain the true velocity constant k t l . Van’t Hoff l 2 from thermodynamic considerations regarding reaction velocities in liquid systems, showed that, if the solubility of the reacting substance is taken as the unit of concentration measurement, the reaction velocities in different solvents will be independent of the nature of the medium. These considerations, accordingly, make the reaction velocity a function of the activities of the reactants. Van’t Hoff, however, did not apply this reasoning to cases of homogeneous catalysis, in which the activity coefficients of the reacting substances may be influenced by different concentrations of the catalyst. The above deduction is thus an extension of the views of Van’t Hoff to cases where the solvent is a solution of the catalyst, and the result will be of particular importance in studies on the neutral salt effect, where there is a considerable “salting out” of the reacting substance by the added salt. Experimental The experimental method employed throughout in determining the velocity constants was the same as that usually employed, namely, the determination from time to time of the total acid present in the esterhydrochloric acid mixture by means of sodium and barium hydroxide solutions. Densities of all the solutions were determined so that the calculations could be made on either a weight or a volume normal basis. Further, all solutions were so standardized that it was possible to compute the absolute quantities of all the molecular species present a t any time during the course of the reaction. Since calculations were made by both the monomolecular formula and by the general kinetic equation for the reaction, it will be necessary to discuss the procedure in some detail. Materials.-Ethyl acetate was prepared from alcohol and acetic acid and purified in the usual way. After repeated fractional distillation, the portion which passed over between 77’ and 78’ was collected for the investigation. Analysis of this fraction gave 98.51% of saponifiable ester, free from acetic acid. Tests for free acetic acid were made from time to time during the course of the investigation and in no case was it Found present. Constant-boiling hydrochloric acid was made, diluted to about 3 M , and checked by gravimetric analysis. All solutions of the acid were made from this sample by the weight method. The solutions of the acid were correct t o within *0.1% of the total hydrochloric acid content. Conductivity water freed from carbon dioxide by boiling was employed. All the necessary precautions were employed in making up and keeping the sodium and barium hydroxide solutions used in the work.
Method of Procedure.-Each determination was carried out in a 250cc. flask, and in every determination 200 g. of water was employed. The molal concentration of the hydrochloric acid (mols of acid in 1000 12 Van’t Hoff, “Lectures on Theoretical and Physical Chemistry,” Arnold, London, 1898, Part I, p. 221.
VeLOCITY OF HYDROLYSIS OF
ETHYL ACETATE
2197
g. of water) varied from 0.01 M to 1.5 M . The same quantity of ethyl acetate was added in each determination in a given series. Thus, in every determination of a given series, the same quantity of water, and the same quantity of ester was employed, the only variable being the hydrochloric acid content. Two series of results were obtained, using 5 cc. and 1 cc. of ester to 100 g. of water, respectively. The reaction was carried out a t 25.00 * 0.01’. The addition of as much as 10 cc. of ester to 200 g. of water caused a noticeable rise in temperature, amounting to 1’ in cases where the molal concentration of hydrochloric acid was 0.5 or higher. Therefore, before making the initial titration, it was necessary to wait until the temperature was reduced to 25’. The velocity measurements were made in the usual way by pipetting out 1Occ. portions from time to time and titrating. Considerable care was exercised throughout all subsequent work. The Kinetics of the Reaction.-In what follows, a very careful study has been made of the velocity constants calculated by both the simplified and approximate monomolecular reaction equation, and the more general kinetic equation which takes into consideration the reverse reaction. I . The Kinetics of the First O r d q Reaction.-The general equation for the kinetics of the reaction RCOOR’ HzO e RCOOH R’OH in going from left to right, assuming that the activities of the 4 molecular species are proportional to their concentrations during the course of the reaction, and that the hydrogen-ion activity remains constant, will be
+
; i l = k ’Ii 13 (A dx
- X ) ( B - X) - k2x2
+
(7)
where dxldt is the velocity, A and R the initial concentrations of ester and water, x the amount of ester changed in a time t, and k”l and kz are the velocity constants of hydrolysis and esterification, respectively. Since the water concentration, B, varies only slightly during the reaction and since the reaction goes nearly to completion when a large quantity of water is present, Equation 7 may be reduced to the much simpler and approximate monomolecular equation dx = k t f I ( A- X) (8) dt
which upon integration takes the well-known form k”,
=
-
1 A -In t A - x
(9)
This equation expressed in terms of the number of cubic centimeters of alkali employed becomes
2198
HERBERT S. HARNED AND ROBERT PFANSTW,
where T , is a number slightly greater than the final titration,'* Tothe initial titration, and T the titer a t a time t. 2. The General Kinetic Equation.-kz may be eliminated from Equation 7 by employing the relation ki = kYiK
(11 )
where K is the equilibrium constant. Substituting for ka in (7) gives
2
= k'l(A
- x ) ( B - x ) - k''lKx2
(12)
which on rearrangement and integration becomes dx A + B x I
AB 1-K
= k"i(1
- K)t + C
(13)
By letting a+B=-
1-K A + B
(14)
and cup =-1 A B
-X the expression on the left side of (13) may be integrated, and the constant of integration may be evaluated from the fact that when t = 0, x = 0. Substituting the values for Q! and bobtained from (14) and (15) in this equation, the general kinetic equation is obtained, which upon simplification becomes in which
I=
P+ =
(A
2.303
d(A
+ B)3 - U B ( 1 - K ) '
+ B ) - d ( A + B)z - U B ( 1 - K )
Griffith and LewisQindicate how Equation 7 may be integrated by a different substitution. Knoblauchls integrated a similar equation by a different substitution. Calculations and Tables of Velocity Constants Computed by Monomolecular Equation.-In computing k " ~ according , t o the monomolecular Equation 10, Too represents the quantity of alkaline hydroxide solutions which would be required for titration after complete hydrolysis. Since the reaction does not go to completion, T cannot be determined experimentally. Therefore, T was calculated in each experiment as follows. The weight of 10 cc. of the solution, delivered from the pipet used in each titration was determined. Let this be called "a". I n the preparation '1
l6
Explained in a later section. Knoblauch, Z . physik. Chem., 22, 268 (1897).
2199
VELOCITY OF HYDROLYSIS OF ETHYL ACETATE
of the solutions, the weight of each component was known. Let “b” equal the weight of the water, “d” the weight of the hydrochloric acid, and “e” the weight of the ester in the reaction flask. Then
a
b+d+eXd
a
X e is the numb+d+e ber of grams of ethyl acetate (assuming no hydrolysis) in each pipet. Therefore, the alkali equivalent of both the hydrochloric acid and ethyl acetate in cubic centimeters, or T is readily obtained. It is important to note that, employing this value for Too gives values for the velocity constant which are lower than those obtained by taking for T co the titration when equilibrium is reached. Although the velocity constants show a greater variation in value (due to the influence of the reverse reaction) as the reaction approaches equilibrium than is apparent when the final titration value for Too is employed in the calculations, the values for the velocity constants a t the beginning of the reaction are somewhat more consistent. The results for k ’ ’ ~will be lower than the other results in the literature for this reason. The values of the velocity constants for the different concentrations are given in Table 11. They are the mean of the constants for the first
is the number of grams of hydrochloric acid, and
TABLE11 MONOMOLEC~LAR VELOCITYCONSTANTS (1) 0.470 N Ester (k’1Fa) X 106 (k’1Fe) X 106
a
(k’1Fe)a X 106 ~1 CP 6.11 611 642 18.30 610 641 30.00 600 630 41.79 597 627 60.15 601 632 91.1 607 639 122.2 611 643 185.5 618 653 312.4 625 661 450 643 681 640 640 6% 1006 671 723 (2) 0.100 N Ester 0 00987 6.37 0.010 637 645 0 02961 18.96 632 0 030 640 0 050 0.0493 31.74 644 634 0.0690 44.44 0.070 635 644 0.0985 63.56 0.100 636 645 0.1477 95.54 0.150 647 637 0.1966 129.0 0.200 656 645 0.2944 197.2 0.300 657 670 Obtained by Equation 9 and equals 2.303 times the values in Table I. Cl
62
0.010 0.030 0.050 0.070 0.100 0 150 0.200 0.300 0.500 0.700 1.ooo 1.500
0.00952 0.02857 0.04759 0.06666 0.0951 0.1425 0.1900 0.2840 0.4726 0.6604 0.9354 1.391
2200
HERBERT S. HARNED AND ROBERT PPANSTLE&
half of the reaction which in all cases gave concordant values. The constants for the two series differing in concentration of ester employed, are given. Two determinations of the velocity constants were made a t each concentration of acid and the mean value recorded. k t f l or kf,Fe is the mean monomolecular velocity constant, c1 is the molal concentration of hydrochloric acid, and cz is its normal concentration. Calculation of the Equilibrium Constant.-In the calculation by means of the general equation, it is necessary to employ a value for the equilibrium constant. The classic work of Berthelot and St. Gilles leads '~ an equimolecular mixture of alcohol to the value of 4. K n o b l a ~ c h , using and water, a high concentration of ester, and hydrochloric acid as catalyst, obtained 2.67. Jones and I,apworthI6 found that, in the presence of large quantities of hydrochloric acid (over 1M ) , the equilibrium constant was considerably greater than 4. Since no definite information regarding the value of K for the ethyl acetate reaction in the presence of hydrochloric acid a t the concentrations here employed was available, the equilibrium constant was determined a t each acid concentration. Since, under the experimental conditions, the ethyl acetate is 9770 hydrolyzed, great accuracy could not be obtained. The observed values for K were 3.39,3 ,E, 3.50, 3.89, 3.87, 3.61, 4.01, 4.00, 3.93, 3.65, and 3.35 a t the molal concentrations 0.01, 0.03, 0.05, 0.07, 0.10, 0.15, 0.20, 0.30, 0.50, 0.70, 1.00, respectively. Since there was no apparent increase or decrease of the equilibrium constant within the limits of the hydrochloric acid concentrations, and since the mean value (3.74) checks within the experimental error the value of Berthelot and St. Gilles, 4, has been employed in all subsequent calculations. Method of Calculation by the General Equation and Tables of Velocity Constants Computed by the General Equation.-In order to employ Equation 16, it is necessary to obtain the values of A , the initial concentration of ester, 3 the initial concentration of water, and x, the concentration of ester changed in a time t. A and B were readily obtained since the weights of the ester and water, and the densities of the solutions were known, Their calculation needs no explanation. Therefore, it is necessary only to show how x is calculated and how a slight change is made in T o and in the first reading of t. From Equation 16, when t equals 0, x must equal 0. Under the experimental conditions, it is impossible to start the experiment a t the beginning of the hydrolysis. When the first titration is made, some ester has hydrolyzed and x , therefore, has an appreciable value when t equals 0. Therefore, To, the initial titration, is corrected to a value which will make x equal to 0, and t is corrected so as to make the starting time of the reaction the moment when x equals 0. The following explanation will show how this correction is made. Let 18
Jones and Lapworth, 1.Chem. Soc., 99, 1427 (1911).
2201
VELOCITY OF HYDROLYSIS OF ETHYL ACETATE
the initial titration be TO. Calculate T co. Then the ester equivalent, T E ,of the contents of one pipet of the solution in terms of cubic centimeters of alkali is calculated. Let T, - T E = T'o. T'o is less than T oby a quantity of alkali equivalent to the acetic acid formed from the beginning of the hydrolysis up to the time of the first titration. From this, the lapse of time from the beginning of hydrolysis up to the time of the first titration may be computed from the equation t = - 2.303 R"1
log
(Tw-T'o) (Tw- To)
This time is added to the time period of each subsequent titration. The T'o - T = x. Table I11 contains value of x for each titration will be TE
a comparison of the velocity constant obtained from the first order equation and from Equation 16. k"l equals k',F,. TABLE 111 COMPARISON OP VELOCITY CONSTANTS BY MONOMOLECULAR AND GENERAL EQUATION c1 = 0.20 cz = 0.1897 Equation 10 Equation 16
1
Time Min.
..
71 158 259 371 491 638 837 1010
--
2
....
8.47 17.82 27.48 36.71 45.42 54.30 63.90 70.75 97.00" .. 100.45' End-point.
'Te.
3
T - T O k'IFe
I = 0.04117 m = 0.1506 5
4
X
lo3
...
- TIo
Time
T
48 119 206 307 419 539 686 885 1058
6.03 14.50 23.85 33.51 42.74 51.45 60.33 69.93 76.78 103. 03d 106.46'
6 x g.
~t=
-
-2.738 7 k'1Fs X10'
0.02675 0.06433 0.1058 0.1486 0.1895 0.2283 0.2676 0.3102 0.3406 ... .. 0.4570" ... .. 0.4724" Tw-To. End-point. x' =equilibrium value of x. A =initial ester
1.240 1.236 1,234 1.226 1.226 1.218 1.208 1.206
2.340 2.345 2.345 2.337 2.347 2.335 2.335 2.338 2.353
...
...
quantity.
From this table, it is seen that the time of hydrolysis began 48 minutes before the first titration was made and, in that time, enough acetic acid was formed to neutralize 6.03 cc. of alkali. The time in Col. 4 was obtained by adding 48 to the values in Col. 1, and the values in Col. 5 were obtained by adding 6.03 to the values in Col. 2. Equation 16 was proved to give constant values for K'lF, when calculated from the titrations near the equilibrium point of the reaction. In Table I V are compiled the mean values of krlF,, obtained by Equation 16; c1 is the molal concentration, and c2 is the normal concentration of the hydrochloric acid. I n Cols. 3 and 4 have been included the observed velocity constants, and in Col. 5 their mean values.
2202
HERBERT S. HARNED AND ROBERT PFANSTIEL
Table IV shows that in the first series, corresponding to an initial concentration of ester of 0.47 N , the values obtained for the ratios of the velocity constants to the hydrochloric acid normalities are greater than they are in the second series, which corresponds to an initial ester concentration of 0.100 N . If the activity of the hydrogen ion is not changed by increasTABLEIV VELOCITY CONSTANTS BY THE
1
2
61
C2
k’iFe (Obs.)
1.500
0.00952 0.02857 0.0476 0.0667 0.0951 0.1425 0.1900 0.2840 0.473 0.660 0.935 1.391
0.010 0.030 0.050 0,070 0.100 0.150 0.200 0.300
0.00987 0.02961 0.0493 0.0690 0.09% 0. I477 0.1966 0.2944
0.010 0.030 0.050 0.070 0.100 0.150 0.200 0.300 0.500 0.700 1.000
GENERALKINETICEQUATION
0.47 N Ester 3 4
5
6 7 k’iFe X l@k’fFe X 10’
X 10’
(Obs.)
1.168 1.165 3.462 3.422 5.729 5.728 7.95 7.98 11.49 11.44 17.41 17.31 23.42 23.12 35.68 35 00 59.90 60.20 86,23 85.83 124.7 125.5 196.1 ..... 0.100 N Ester 1.166 1.166 3.460 3.440 5.77 5.79 8.06 8.13 11.55 11.56 17.50 17.64 23.61 23.69 36.00 35.90
61
62
(Mean)
1.167 3.442 5.729 7.97 11.46 17.36 23.27 35.34 60.05 86.03 125.2 196.1
116.7 114.7 114.5 113.9 114.6 115.8 116.3 117.8 120.1 122.9 125.2 130.8
122.6 120.5 120.4 119.6 120.5 121.8 122.5 124.5 127.1 130.2 133.8 141.0
1.166 3.450 5.78 8.09 11.55 17.57 23.65 35.95
116.6 115.0 115.6 115.6 115.6 117.1 118.3 119.8
118.2 116.5 117.3 117.3 117.4 119.0 120.3 122.1
ing the ester concentration and there is no other catalytic influence, then, according to the general kinetic equation, a change in ester concentration a t constant hydrochloric acid normality should not affect the velocity constant. This difference is, however, in agreement with the results of G r B t h and Lewisg who, working a t constant volume and constant hydrochloric acid concentration, found that the velocity increased with increasing ester concentration. They ascribed the cause t o a negative catalytic effect of the water.
Discussion The point of view adopted in this investigation is based onthermodynamic reasoning.& Further, the assumption is made that all the catalytic &e& of the hydrochloric acid is caused by the hydrogen ion. An inspection of Tables I, I1 and I V shows that, in each case, the ratio of the
VELOCITY OF HYDROLYSIS OF ETHYL ACETATE
2203
velocity constant to the concentration of the hydrochloric acid has a minimum value somewhere between 0.06 M and 0.100 M hydrochloric acid concentration. This fact is supported by the work of others, and in every instance is verified in the present investigation.‘? The individual hydrogen-ion activity coefficient in pure solutions of hydrochloric acid, according to the assumptions mentioned in the introduction, will be given by the equationla log FH = 0.330 CI
- 0.284 cP4’l
(17)
where FHis the activity coefficient of the hydrogen ion, and c1 the molal concentration of the hydrochloric acid. In Fig. 1 are given the plots of kflFe/cl against log CI, and also FHagainst log cl. It is clear that with increasing acid concentration, the value of
Fig. 1.
the ordinate first passes through a minimum and then rises rapidly in both cases. The minimum of each curve occurs between 0.07 M and 0.200 M concentration of hydrochloric acid. I n dilute solutions F H decreases more rapidly than kflFe/cl with increasing acid concentration, while in concentrated solutions i t increases more rapidly. Therefore, if the values of kflFe are divided by the activity of the hydrogen ion of pure hydrochloric acid solution, a constant will not be obtained. This 1’ It was thought that possibly the rise in the ratio of the velocity constant, K‘i F ., to the concentration at the low concentrations, could be caused by the catalytic effect of the increase in number of hydrogen ions formed during the course of the reactian. This is not the case because k’l Fa, calculated by either the monomolecular or the general equation, had as high values a t the beginning of the reaction as a t any time during the course of the reaction. In other words, the present experimental method failed t o detect such an autocatalysis. Harned, THISJOURNAL, 44, 252 (1922).
2204
HJ3RBERT S. HARNED AND ROBERT PFANSTIEL
is shown by the results in Table V. In Col. 1 are the molal concentrations of hydrochloric acid, and in Col. 2 are the corresponding activity coefficients of the hydrogen ion of pure hydrochloric acid solution. Col. 3 contains the activity of the water molecule a t various acid concentrations, computed from the vapor pressure of water over the hydrochloric acid solutions.** Col. 4 gives the ratios of the velocity constants to the corresponding hydrogen-ion activities, and Col. 5 contains the ratios of the velocity constants to the products of the hydrogen-ion and water activities. l9 TABLEV VELOCITY CONSTANT ACTIVITY RATIOS 1 2 3 4 5 p" (V~F.) x 104 P ~ F . x 104 aw = c1 Fx PO aa ama 0.010 0.935 ... 1.248 1.248 ... 1 ,270 1.270 0.030 0.903 .. 1.292 1.293 0.050 0.886 0.070 0.875 ... 1.302 1.303 0.100 0.868 0.997 1.320 1.324 0.150 0.858 0.995 1.350 1.357 0 * 993 1.257 1.367 0.200 0.857 0,300 0.867 0.990 1.359 1.373 0.500 0.914 0.983 1.314 1.337 0.700 0.979 0.975 1.255 1.287 1.000 1.112 0.964 1.126 1.168 1,500 1.416 0.942 0,924 0.980 fi Is the partial vapor pressure of water, and po is the vapor pressure of pure water.
It is clear from the above table that the values of
('z) and
( '3) aHaw
are not constant, but have a maximum a t 0.3 M acid concentration; aH is the activity of the hydrogen ion in pure hydrochloric acid solution; but, as already pointed out,
):(t-
should not be constant if F, varies
with the acid concentration, or FH with ester concentration. The value of F, in solutions of hydrochloric acid can be obtained theoretically from either the measurement of the partial vapor pressure of the ester over the solution, or from its solubility. According to our assumptions, it has been shown that k F . S should be constant if a, enters to the first power, a Haw and if alH is the true activity of the hydrogen ion in the solution. Consequently, if the solubility decreases with increasing acid concentration at the higher dilutions of the acid, the correction for F, will be in the right direction. Determinations of the solubility are difficult on account of hydrolysis. A number of determinations showed that the solubility 19
It is possible that a, should enter to 8 higher power.
VELOCITY OF HYDROLYSIS OF ETHYL ACETATE
2205
does decrease as the acid concentration increases up to a concentration of 0.3 M and this decrease is of the same order of magnitude as the increase of
(E')An attempt
to determine
a'H
by electromotive-force
aHaw
measurements was made but the results have not been included on account of uncertainties caused by liquid-junction potentials and the high partial vapor pressure of the ethyl acetate. The results obtained up to the present, however, do not vitiate any of the conclusions but substantiate them to a limited extent. The present study can only be regarded as a preliminary treatment of this complicated problem, the solution of which would require an accurate knowledge of the activity coefficients and concentrations of all the ionic and molecular species present. In conclusion, it is thought that the minimum in the velocity constant-log c1 plot is contributory evidence of the theory of the independent activity coefficients as developed by MacInnes and Harned. * On the other hand, it is thought that further evidence has been obtained for the activity theory of homogeneous catalysis.
summary 1. The monomolecular velocity constants of hydrolysis of ethyl acetate at many different hydrochloric acid concentrations have been accurately determined a t 25". 2 , A solution of the general equation for the velocity of hydrolysis has been obtained. 3. The velocity constants have been computed by the general equation. 4. In four series of measurements, i t has been found that the plot of the velocity constants divided by the molal concentration of hydrochloric acid against log c1 (c1 equals the molal concentration of the hydrochloric acid) shows a minimum a t 0.07 to 0.08 M concentration of the acid. This is similar to the plot of the individual hydrogen-ion activity coeficient against log c1 which has a minimum a t 0.15 M to 0.18 M acid concentration. 5. It has been shown that the velocity constant divided by the product oi the activities of the hydrogen ion and the water molecule is not a constant a t different acid concentrations but has a maximum a t 0.3 M hydrorhforic acid concentration. 6 . Some factors which may cause this deviation from constancy have been suggested. 7 . The kinetics of hydrolysis of ethyl acetate is very complex, but it is thought that enough evidence has been obtained to show that the method o€ attacking the problem employed in this investigation is in a general way correct. PIIII,ADELPHIA, PENNSYLVANIA
